Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON):

Solution:
import sys

def half_is_triangular(n):

    if n % 2:
        return False
    
    begin, end = 1, n
    
    while begin != end - 1:
        
        middle = (begin + end) / 2
        
        candidate = middle**2 + middle
        
        if candidate < n:
            begin = middle
        elif candidate > n:
            end = middle
        else:
            return True
    
    return True if begin**2 + begin == n else False

def main():
    
    n = int(sys.stdin.readline().strip())
    n *= 2
    
    for i in range(1, 45000):
    
        second_number = n - i**2 - i
        
        if second_number <= 0:
            break
        if half_is_triangular(second_number):
            return True
    
    return False
    
if __name__ == "__main__":
    print ("YES" if main() else "NO")